TSTP Solution File: SEU305+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:32:53 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   59 (  18 unt;   0 def)
%            Number of atoms       :  242 (  55 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  277 (  94   ~;  99   |;  65   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   72 (  57   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f501,plain,
    $false,
    inference(subsumption_resolution,[],[f498,f112]) ).

fof(f112,plain,
    sK1 != sK2,
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ( sK1 != sK2
    & below(sK0,sK2,sK1)
    & below(sK0,sK1,sK2)
    & element(sK2,the_carrier(sK0))
    & element(sK1,the_carrier(sK0))
    & join_semilatt_str(sK0)
    & join_commutative(sK0)
    & ~ empty_carrier(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f47,f87,f86,f85]) ).

fof(f85,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( X1 != X2
                & below(X0,X2,X1)
                & below(X0,X1,X2)
                & element(X2,the_carrier(X0)) )
            & element(X1,the_carrier(X0)) )
        & join_semilatt_str(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( X1 != X2
              & below(sK0,X2,X1)
              & below(sK0,X1,X2)
              & element(X2,the_carrier(sK0)) )
          & element(X1,the_carrier(sK0)) )
      & join_semilatt_str(sK0)
      & join_commutative(sK0)
      & ~ empty_carrier(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( X1 != X2
            & below(sK0,X2,X1)
            & below(sK0,X1,X2)
            & element(X2,the_carrier(sK0)) )
        & element(X1,the_carrier(sK0)) )
   => ( ? [X2] :
          ( sK1 != X2
          & below(sK0,X2,sK1)
          & below(sK0,sK1,X2)
          & element(X2,the_carrier(sK0)) )
      & element(sK1,the_carrier(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ( ? [X2] :
        ( sK1 != X2
        & below(sK0,X2,sK1)
        & below(sK0,sK1,X2)
        & element(X2,the_carrier(sK0)) )
   => ( sK1 != sK2
      & below(sK0,sK2,sK1)
      & below(sK0,sK1,sK2)
      & element(sK2,the_carrier(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( X1 != X2
              & below(X0,X2,X1)
              & below(X0,X1,X2)
              & element(X2,the_carrier(X0)) )
          & element(X1,the_carrier(X0)) )
      & join_semilatt_str(X0)
      & join_commutative(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( X1 != X2
              & below(X0,X2,X1)
              & below(X0,X1,X2)
              & element(X2,the_carrier(X0)) )
          & element(X1,the_carrier(X0)) )
      & join_semilatt_str(X0)
      & join_commutative(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,negated_conjecture,
    ~ ! [X0] :
        ( ( join_semilatt_str(X0)
          & join_commutative(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,the_carrier(X0))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( ( below(X0,X2,X1)
                    & below(X0,X1,X2) )
                 => X1 = X2 ) ) ) ),
    inference(negated_conjecture,[],[f35]) ).

fof(f35,conjecture,
    ! [X0] :
      ( ( join_semilatt_str(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( ( below(X0,X2,X1)
                  & below(X0,X1,X2) )
               => X1 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).

fof(f498,plain,
    sK1 = sK2,
    inference(superposition,[],[f489,f323]) ).

fof(f323,plain,
    sK2 = join(sK0,sK1,sK2),
    inference(subsumption_resolution,[],[f322,f105]) ).

fof(f105,plain,
    ~ empty_carrier(sK0),
    inference(cnf_transformation,[],[f88]) ).

fof(f322,plain,
    ( sK2 = join(sK0,sK1,sK2)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f321,f107]) ).

fof(f107,plain,
    join_semilatt_str(sK0),
    inference(cnf_transformation,[],[f88]) ).

fof(f321,plain,
    ( sK2 = join(sK0,sK1,sK2)
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f320,f108]) ).

fof(f108,plain,
    element(sK1,the_carrier(sK0)),
    inference(cnf_transformation,[],[f88]) ).

fof(f320,plain,
    ( sK2 = join(sK0,sK1,sK2)
    | ~ element(sK1,the_carrier(sK0))
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f318,f109]) ).

fof(f109,plain,
    element(sK2,the_carrier(sK0)),
    inference(cnf_transformation,[],[f88]) ).

fof(f318,plain,
    ( sK2 = join(sK0,sK1,sK2)
    | ~ element(sK2,the_carrier(sK0))
    | ~ element(sK1,the_carrier(sK0))
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(resolution,[],[f125,f110]) ).

fof(f110,plain,
    below(sK0,sK1,sK2),
    inference(cnf_transformation,[],[f88]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( ~ below(X0,X1,X2)
      | join(X0,X1,X2) = X2
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( below(X0,X1,X2)
                  | join(X0,X1,X2) != X2 )
                & ( join(X0,X1,X2) = X2
                  | ~ below(X0,X1,X2) ) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( join_semilatt_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).

fof(f489,plain,
    sK1 = join(sK0,sK1,sK2),
    inference(forward_demodulation,[],[f480,f448]) ).

fof(f448,plain,
    sK1 = join_commut(sK0,sK1,sK2),
    inference(forward_demodulation,[],[f447,f327]) ).

fof(f327,plain,
    sK1 = join(sK0,sK2,sK1),
    inference(subsumption_resolution,[],[f326,f105]) ).

fof(f326,plain,
    ( sK1 = join(sK0,sK2,sK1)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f325,f107]) ).

fof(f325,plain,
    ( sK1 = join(sK0,sK2,sK1)
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f324,f109]) ).

fof(f324,plain,
    ( sK1 = join(sK0,sK2,sK1)
    | ~ element(sK2,the_carrier(sK0))
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f319,f108]) ).

fof(f319,plain,
    ( sK1 = join(sK0,sK2,sK1)
    | ~ element(sK1,the_carrier(sK0))
    | ~ element(sK2,the_carrier(sK0))
    | ~ join_semilatt_str(sK0)
    | empty_carrier(sK0) ),
    inference(resolution,[],[f125,f111]) ).

fof(f111,plain,
    below(sK0,sK2,sK1),
    inference(cnf_transformation,[],[f88]) ).

fof(f447,plain,
    join(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2),
    inference(forward_demodulation,[],[f440,f365]) ).

fof(f365,plain,
    join_commut(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2),
    inference(resolution,[],[f359,f109]) ).

fof(f359,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(sK0))
      | join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0) ),
    inference(subsumption_resolution,[],[f358,f105]) ).

fof(f358,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
      | ~ element(X0,the_carrier(sK0))
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f357,f106]) ).

fof(f106,plain,
    join_commutative(sK0),
    inference(cnf_transformation,[],[f88]) ).

fof(f357,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f346,f107]) ).

fof(f346,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_semilatt_str(sK0)
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(resolution,[],[f143,f108]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(X0))
      | join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & join_semilatt_str(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
     => join_commut(X0,X1,X2) = join_commut(X0,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).

fof(f440,plain,
    join(sK0,sK2,sK1) = join_commut(sK0,sK2,sK1),
    inference(resolution,[],[f434,f109]) ).

fof(f434,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(sK0))
      | join_commut(sK0,X0,sK1) = join(sK0,X0,sK1) ),
    inference(subsumption_resolution,[],[f433,f105]) ).

fof(f433,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join(sK0,X0,sK1)
      | ~ element(X0,the_carrier(sK0))
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f432,f106]) ).

fof(f432,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join(sK0,X0,sK1)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f421,f107]) ).

fof(f421,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK1) = join(sK0,X0,sK1)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_semilatt_str(sK0)
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(resolution,[],[f144,f108]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(X0))
      | join_commut(X0,X1,X2) = join(X0,X1,X2)
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( join_commut(X0,X1,X2) = join(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( join_commut(X0,X1,X2) = join(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ join_commutative(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & join_semilatt_str(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
     => join_commut(X0,X1,X2) = join(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).

fof(f480,plain,
    join(sK0,sK1,sK2) = join_commut(sK0,sK1,sK2),
    inference(resolution,[],[f437,f108]) ).

fof(f437,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(sK0))
      | join_commut(sK0,X0,sK2) = join(sK0,X0,sK2) ),
    inference(subsumption_resolution,[],[f436,f105]) ).

fof(f436,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK2) = join(sK0,X0,sK2)
      | ~ element(X0,the_carrier(sK0))
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f435,f106]) ).

fof(f435,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK2) = join(sK0,X0,sK2)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f422,f107]) ).

fof(f422,plain,
    ! [X0] :
      ( join_commut(sK0,X0,sK2) = join(sK0,X0,sK2)
      | ~ element(X0,the_carrier(sK0))
      | ~ join_semilatt_str(sK0)
      | ~ join_commutative(sK0)
      | empty_carrier(sK0) ),
    inference(resolution,[],[f144,f109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 10:53:16 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (27904)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (27910)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.38  % (27907)WARNING: value z3 for option sas not known
% 0.13/0.38  % (27905)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (27906)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % (27909)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.38  % (27911)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.38  % (27907)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.38  % (27908)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39  TRYING [1]
% 0.13/0.39  TRYING [2]
% 0.13/0.40  TRYING [1]
% 0.13/0.40  TRYING [2]
% 0.13/0.40  TRYING [3]
% 0.13/0.40  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.41  % (27907)First to succeed.
% 0.21/0.41  % (27907)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27904"
% 0.21/0.41  % (27907)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42  % (27907)------------------------------
% 0.21/0.42  % (27907)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.42  % (27907)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (27907)Memory used [KB]: 1048
% 0.21/0.42  % (27907)Time elapsed: 0.031 s
% 0.21/0.42  % (27907)Instructions burned: 29 (million)
% 0.21/0.42  % (27904)Success in time 0.061 s
%------------------------------------------------------------------------------